Finding the Optimal Placement of Evacuation Centers by Antibase Set of Intuitionistic Fuzzy Graph

Abstract

The problem of choosing places for evacuation centers is considered in this paper. We consider the case when the territory model is represented by an intuitionistic fuzzy graph. To solve this problem, the concept of a minimal antibase of such graph is introduced, and on its basis, the concept of an antibase set as an invariant of this graph is introduced too. A method and algorithm for calculating the minimal antibases are proposed and justified. The problem of finding all minimal antibases of the graph allows us to solve the task of determining the antibase set. The paper considers a numerical example of finding the antibase set of an intuitionistic fuzzy graph. The task of choosing the places of evacuation centers in an optimal way depends on their number. The calculation of the minimal antibase set allows us to directly solve this problem.